Certificate of residence.
Official confirmation of residence, which some landlords request in addition.
The certificate of residence (Wohnsitzbescheinigung; depending on the commune also called Wohnsitzbestätigung or Niederlassungsbestätigung) is issued by the residents' office (Einwohnerkontrolle) of the commune where you live. It confirms that you are registered there and since when. You register within 14 days of moving in; federal law requires the cantons to set this rule (art. 11 RHG). Some landlords ask for the certificate as an extra document.
Cost and time: set by each commune; you can often get it at the counter or online.
Foreign nationals: your residence permit (B, C or L) shows your residence status, and landlords usually ask for the permit itself. Weekly residents, who keep their main home elsewhere, are registered only for their stay and get a different confirmation.
General information, not legal advice.